Several prior art systems are known providing for building structures using pentagonal, hexagonal, cubic and icosahedral symmetry.
In two-dimensions, U.S. Pat. Nos. 143,835 to Muller, 4,343,471 to Calvert, and 4,133,152 to Penrose demonstrate pentagonal symmetry. U.S. Pat. No. 3,637,217 to Kent demonstrates hexagonal symmetry.
In three-dimensions, U.S. Pat. Nos. 3,600,825 to Pearce, 4,129,975 to Gabriel, and 4,183,190 to Bance demonstrate cubic symmetry. U.S. Pat. Nos. 3,722,153 to Baer and 4,113,256 to Hutchings demonstrate icosahedral symmetry. The disclosures of these eight patents are hereby incorporated by reference.
In articles published by Kramer and by Mosseri and Sadoc, icosahedral symmetry is used to create building structures, with Kramer using seven elementary cells and Mosseri and Sadoc using four and six elementary cells.
However, none of these systems discloses or suggests breaking down a building structure to a versatile basic set of polygonal planar members which can be combined to form polyhedra that in turn are combined to fill three-dimensional space periodically or non-periodically.